Robust accurate transient slip estimation is fundamental to achieving a significant measure of success in several types of motor analysis. Established techniques often explicitly or implicitly assume stationary or quasi-stationary motor operation. In practicality, however, motor and load environments are dynamic and dependent on a myriad of variables, such as internal and external temperature, varying load dynamics, fundamental frequency and voltage, etc. The cumulative effects of such variations can have a significant detrimental effect on many types of motor analysis.
Model Referencing Adaptive System (MRAS) is a method of iteratively adapting an electrical model of a three-phase induction motor with significant performance advantages over competitive approaches assuming quasi-stationary motor operation, as the assumption of stationary operation is often violated, with detrimental effect on model accuracy. MRAS is highly dependent upon availability of robust transient slip estimation. Applications benefiting from accurate transient slip estimation include, but are not limited to, synthesis of high quality electrical and thermal motor models, precision electrical speed estimation, dynamic efficiency and output power estimation, and inverter-fed induction machines employing vector control.
Slip estimation can be performed by passive analysis of the voltage and current signals of a three-phase induction motor, and commonly available motor-specific parameters. In a stationary environment, slip estimation accuracy is optimized by increasing the resolution of the frequency, or degree of certainty of the frequency estimate. As motor operation is typically not stationary, robust slip estimation also depends upon retention of sufficient temporal resolution, such that the unbiased transient nature of the signal is observed.
Frequency estimation is commonly performed by Fourier analysis. Fourier analysis is frame-based, operating on a contiguous temporal signal sequence defined over a fixed period of observation. Frequency resolution, defined as the inverse of the period of observation, can be improved by extending the period of observation, and moderate improvement in effective frequency resolution can be realized through local frequency interpolation and other techniques that are generally dependent on a priori knowledge of the nature of the observed signal.
In Fourier analysis, it is implicit that source signals are stationary over the period of observation, or practically, that they are stationary over contiguous temporal sequences that commonly exceed the period of observation in some statistical sense. Fourier analysis can be inappropriate for application in environments where a signal of interest violates the stationary condition implicit in the definition of a specific period of observation. Such instances may result in an aggregate frequency response and loss of transient information determined to be important to analysis. Fourier analysis presents a temporal range versus frequency resolution dilemma. At periods of observation to resolve a saliency harmonic frequency with sufficient accuracy, the stationary condition is violated and important transient information is not observable.
An effective saliency harmonic frequency resolution of less than 0.1 Hz may be defined to be minimally sufficient, resulting in a requisite period of observation of 10 seconds, which may be reduced to no less than 1.0 second through application of local frequency interpolation. However, saliency harmonic frequency variations exceeding 10.0 Hz are not uncommon. The relative transient nature of such signals violates the stationary condition requirement implicit in the definition of the minimum period of observation. Fourier analysis is not suitable for employment in robust accurate slip estimation, in applications where preservation of significant transient temporal response is important.
In a stationary environment, frequency estimation accuracy is optimized by increasing the resolution of the frequency, or degree of certainty of the frequency estimate. As motor operation is typically not stationary, robust frequency estimation also depends upon retention of sufficient temporal resolution, such that the unbiased transient nature of the signal is observed. Conventional frequency estimation methods, including the Fourier transform, provide aggregate frequency estimations, which lack the requisite temporal resolution and require impractically long periods of observation to provide minimally sufficient frequency resolution. There is therefore a continuing need for more robust and efficient means of accurately estimating the instantaneous frequency of a dynamic complex signal.